Problem: Solve for $p$. Give an exact answer. $4+2p=10\left(\dfrac35p-2\right)$ $p =$
We need to manipulate the equation to get $ p $ by itself. $\begin{aligned} 4+2p &= 10\left(\dfrac35p-2\right) \\\\ 4+2p &= 6p-20~~~~~~~~~~\gray{\text{Distribute}}\\\\ 4+2p{-6p} &= 6p-20{-6p} ~~~~~~~~~~\gray{\text{Subtract 6p from each side}}\\\\ 4-4p &=-20 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ 4-4p{-4} &=-20 {-4} ~~~~~~~~~~\gray{\text{Subtract 4 from each side}}\\\\ -4p &=-24 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ \dfrac{-4p}{{-4}}&= \dfrac{-24}{{-4}}~~~~~~~~~~\gray{\text{Divide each side by -4}} \\\\ p &= {6} ~~~~~~~~~~\gray{\text{Simplify}}\\\\ \end{aligned}$ The answer: $ p = { 6 }~~~~~~~~$ [Let's check our work!]